大 EMFF Vehicle Conceptual Model SRl In the Far field, dipoles add as vectors Each vehicle will have 3 orthogonal electromagnetic coils These will act as dipole vector components and allow the magnetic dipole to be created in any direction Steering the dipoles electronically will decouple them from the spacecraft rotational dynamics A reaction wheel assembly with 3 orthogonal wheels provides counter torques to maintain attitude DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 EMFF Vehicle Conceptual Model EMFF Vehicle Conceptual Model • In the Far Field, Dipoles add as vectors • Each vehicle will have 3 orthogonal electromagnetic coils – These will act as dipole vector components, and allow the magnetic dipole to be created in any direction • Steering the dipoles electronically will decouple them from the spacecraft rotational dynamics • A reaction wheel assembly with 3 orthogonal wheels provides counter torques to maintain attitude
大 Outline Motivation Fundamental Principles MIT EMFFORCE Testbed Governing Equations Design Trajectory Mechanics Calibration Stability and Control Movie Mission Applicability Space Hardware Design Sparse arrays ssues Filled Apertures Thermal control other Proximity operations Power System Design High B-Field Effects Mission Analyses Sparse arrays · Conclusions Filled Apertures other Proximity operations DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Outline Outline • Motivation • Fundamental Principles – Governing Equations – Trajectory Mechanics – Stability and Control • Mission Applicability – Sparse Arrays – Filled Apertures – Other Proximity Operations • Mission Analyses – Sparse Arrays – Filled Apertures – Other Proximity Operations • MIT EMFFORCE Testbed – Design – Calibration – Movie • Space Hardware Design Issues – Thermal Control – Power System Design – High B-Field Effects • Conclusions
大 Magnetic Dipole Approximation S5 The interaction force between two arbitrary magnetic circuits is given by the Law of Biot and savart F d2x[ In general, this is difficult to solve, except for cases of special symmetry Instead. at distances far from one of the circuits the magnetic field can be approximated as a dipole B=Lo A1-H 41 [3(A1) where its dipole strength u, is given by the product of the total current around the loop(amp-turns ) and the area enclosed DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Magnetic Dipole Approximation Magnetic Dipole Approximation • The interaction force between two arbitrary magnetic circuits is given by the Law of Biot and Savart I1 I2 O • In general, this is difficult to solve, except for cases of special symmetry • Instead, at distances far from one of the circuits, the magnetic field can be approximated as a dipole [ ] 11 1 0 53 3 1 1 ( ) 3 3( ) ˆ ˆˆ ˆ 4 4 o r B r rr rr r µ µ µµ µ µ µ π π ⎡ ⎤ ⎛⎞ ⋅ = − = ⋅− ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝⎠ GG G G G where its dipole strength µ1 is given by the product of the total current around the loop (Amp-turns) and the area enclosed
大 Dipole-Dipole Interaction Just as an idealized electric charge in an external electric field can be assigned a scalar potential, so can an idealized magnetic dipole in a static external magnetic field, by taking the inner product of the two U=-2B Continuing the analogy the force on the dipole is simply found by taking the negative potential gradient with respect to position coordinates F=-V,U=V,(2·B)=2V,B In a similar manner, taking the gradient with respect to angle will give the torque experienced by the dipole T=-VOU=H,XB Since the Force results from taking a gradient with respect to position, and the Torque does not, the scaling laws for the two are given as 342 34/2 DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Dipole-Dipole Interaction Dipole Interaction • Just as an idealized electric charge in an external electric field can be assigned a scalar potential, so can an idealized magnetic dipole in a static external magnetic field, by taking the inner product of the two • Continuing the analogy, the force on the dipole is simply found by taking the negative potential gradient with respect to position coordinates • In a similar manner, taking the gradient with respect to angle will give the torque experienced by the dipole • Since the Force results from taking a gradient with respect to position, and the Torque does not, the scaling laws for the two are given as U B = − ⋅ µ2 G G 2 2 ( ) F = −∇ = ∇ ⋅ = ⋅∇ rr r UB B µ µ G G G G TU B = −∇ = × θ µ2 G G 1 2 0 4 3 ~ 2 F s µ µ µ π 1 2 0 3 3 ~ 4 T s µ µ µ π
大 How Far Apart Will They Work? Si Writing the force in terms of the coil radius (r), separation distance(s)and total loop current (), the force scales as 丌 R F~=1r S We see that for a given coil current, the system scales photographically meaning that two systems with the same loop current that are simply scaled versions of one another will have the same force For design, it is of interest to re-write in terms of coil mass and radius, and physical constants 丌 (10 (MCRo) 2R八(s The current state-of-the-art HTS wire has a value of e =14 44 4-ml/kg And the product of coil mass and radius becomes the design parameter DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 How Far Apart Will They Work? How Far Apart Will They Work? • Writing the force in terms of the coil radius (R), separation distance (s) and total loop current (IT), the force scales as • We see that for a given coil current, the system scales ‘photographically’, meaning that two systems with the same loop current that are simply scaled versions of one another will have the same force • For design, it is of interest to re-write in terms of coil mass and radius, and physical constants: • The current state-of-the-art HTS wire has a value of And the product of coil mass and radius becomes the design parameter. 4 2 0 3 ~ 2 T R F I s π µ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 2 4 2 7 2 0 4 3 31 ~ (10 ) ( ) 22 2 CC C C C MI I R F MR R s s π µ π ρ − ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ = ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 14, 444 / CI A m kg ρ ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠